Qualitative Behavior of the Difference Equation xn+1 = αxn-m+ηxn-k+σxn-l+δxn/β+γxn-kxn-l(xn-k+xn-l).

Authors :: El-Moneam, Mohamed Abd
Source :: Fundamental Journal of Mathematics & Applications (FUJMA); Jun2023, Vol. 6 Issue 2, p128-136, 9p
Publication Year :: 2023
Abstract: In this paper, we discuss some qualitative properties of the positive solutions to the following rational nonlinear difference equation x<subscript>n+1</subscript> = αx<subscript>n-m</subscript>+ηx<subscript>n-k</subscript>+σx<subscript>n-l</subscript>+δx<subscript>n</subscript>/β+γx<subscript>n-k</subscript>x<subscript>n-l</subscript>(x<subscript>n-k</subscript>+x<subscript>n-l</subscript>), n = 0,1,2... where the parameters α, β, γ, η, σ ∊(0,∞) while m;k; l are positive integers, such that m, k, l. The initial conditions x<subscript>-m</subscript>....,x<subscript>-k</subscript>...,x<subscript>-l</subscript>...,x<subscript>-1</subscript>...,x<subscript>0</subscript> are arbitrary positive real numbers. We will give some numerical examples to illustrate our results. [ABSTRACT FROM AUTHOR]

Subjects :: QUALITATIVE research
NONLINEAR differential equations
SUBMANIFOLDS
REAL numbers
EQUILIBRIUM

Full Text Access

Tools